Probabilistic and pluralistic learners with mind changes

Abstract

We consider the learning capabilities of FIN- type learners when they are allowed to change their hypothesis at most once. We consider probabilistic learners of this sort as well as pluralistic learners (i.e., teams of deterministic learners). We show for probabilities in the interval (5/6, 1] that the capabilities of the probabilistic learners are precisely divided into intervals of the form (5n+6/6n+7, 5n+1/6n+1] for all n≥0. We show that teams of such learners with plurality r/s (i.e., a team of s learners such that at least τ always successfully learn) are equivalent to probabilistic learners with probability of success τ/s. We also show that at the ratio 5/6 redundancy pays for team learners (i.e., a team with plurality 10/12 is more powerful than a team with plurality 5/6). Moreover, for any r and s with r/s=5/6 we show that any team of learners with plurality r/s is equivalent to a team with plurality 5/6 if r is odd, and to a team with plurality 10/12 if r is even.